As you can see, it punches a pair of holes with a circular part and a longer, thinner part. They're not actually holes, though, as they're attached at one end. The idea is that you bend over the corner of some pieces of paper that you want to keep together, you punch the near-holes in it and then you flatten the corner back out again. The stamped-out paper slides back like a chain lock in a door and keeps your documents together. Neat! It's like a stapler that doesn't use staples, so you don't have to take the staples out of things you want to recycle.
You may have noticed from the dust on it that I don't use it very often. Here's why:
The bits of paper that were nearly stamped out are probably great if you use card or quality paper, but for the kind of cheapo stuff I tend to want to staple together you end up with easily-break-offable bits of chad.
Oh well, I gave it 14 years to make itself useful and it hasn't, so out it goes...